"I cannot be any prouder to take Red Sox Nation to the Hall of Fame with the logo on my plaque," Martinez said in a statement. "I am extremely proud to represent Boston and all of New England with my Hall of Fame career. I'm grateful to all of the teams for which I played, and especially fans, for making this amazing honor come true."
Smoltz was the only player on all of Atlanta's record-setting 14 consecutive playoff teams from 1991-04.
"The Museum staff works with each inductee by suggesting an appropriate logo option, or no logo at all," Hall president Jeff Idelson said in a statement. "For those whose most compelling contributions clearly took place with one team, a logo makes sense. For those whose careers were built significantly among multiple teams, not having a team logo is equally acceptable."
Greg Maddux and Tony La Russa both entered the Hall of Fame last summer with no logos on their plaques after enjoying major success with multiple teams during their careers.
The Class of 2015 will be formally inducted into the National Baseball Hall of Fame on July 26 in Cooperstown, N.Y.
The Associated Press contributed to this report.